Constable struck a memorable opener in the 44th minute and then Danny Rose's penalty, two minutes into first-half stoppage time, doubled the lead after Constable was tripped by Ben Tozer.
"We needed a victory," Wilder said. "We played well and I think it was deserved.
"But Constable was excellent. He was a constant threat, back to where he was when he first came here, rampaging and strong.
"Kitson led the line well and Constable and Sean Rigg either side gave us a good front three.
"I don't think you'll see a better goal in our league this weekend than Constable's.
"We started off the game really well, and passed it well. This is a tough league, there are no givens, so we had to work hard to get a result."
Wilder changed to a 3-4-3 system to accommodate Michael Raynes at the back, with Wright returning from injury.
Wilder said: "I didn't think anybody deserved to be left out, and thought the 3-4-3 system would suit us well.
"Northampton were 90 minutes away from League One, they have a good manager, and when they get their best players back I'm sure they'll be a force."